Can money buy Olympic medals? Not exactly, but a new study by two Goldman Sachs analysts shows that a country's income can have a significant effect on how their athletes perform and — in turn — how many medals they bring home.

The report, called "The Olympics and Economics" by José Ursúa and Kamakshya Trivedi, takes a close look at the effect money and income can have on a country's overall success and within specific sports at the games. They took a look at variables including GDP per capita, the ratio of income to that of the US, democracy and hosting duties, and then studied their combined effects on winning medals.

Turns out, richer countries — those with "superior growth environments and higher incomes"— can usually expect to win more medals.

The sports that were most influenced by those factors were canoeing, diving, fencing, swimming and table tennis. Equestrianism, gymnastics and wrestling were also highly influenced by the factors.

Adversely, sports that aren't as expensive to train for like football, softball and triathlon, were the sports least affected by the factors.

"Progress and improvement in economic growth have historically often equaled progress in sport," the authors wrote. "This trend — with a few economically significant countries winning a bulk of the Olympic medals on offer — has continued in recent times. For example, less than 10 countries participating in the 2008 Beijing Olympics won more than half of the almost 1,000 gold, silver and bronze medals that were distributed."

Additionally, the report proves that "home court advantage" is a very real thing. Countries that are hosting the Olympics tend to bring home more medals than they do when traveling elsewhere for the games, though not in every sport.

"In some cases, hosting the Olympics has meant increasing the number of medals by more than 50 percent with respect to what countries would have otherwise attained," the report stated.

Historically, hosting countries can expect to win about 1.5 to 3 more medals per game in events like cycling, gymnastics, rowing, sailing, swimming and wrestling. Other sports like football, rhythmic gymnastics and water polo don't find as much benefit from the so-called "home court advantage."

But when it comes to a financial win for host countries, the results have been mixed. The 1972 Munich Olympics and the 1976 Montreal Olympics both had significant financial losses. However, the 1984 Los Angeles Olympics, the 1992 Barcelona Olympics and the 1996 Atlanta Olympics all turned a profit, according to the report.

The researchers note that it is too early to predict whether the London Olympics will be profitable, but the city's infrastructure plans for the Games were finished on schedule and even below budget. Though, that very budget has been quite the investment at an estimated £8.5bn (about $13.3 billion).